[Fix] Modify Plan class to update context variables with input (micro…

…soft#685)

### Motivation and Context
Fix issue with invoking plan with both string input and existing
context.

### Description
This pull request refactors the Plan class to update the context
variables with the input string when invoking a plan. This change allows
the plan to use the input as part of the context for executing the plan
steps. The pull request also adds a unit test to verify that the plan
can execute with a given context and input.

Details:
- In Plan.cs, change the InvokeAsync method to create a new SKContext
with empty variables if the context parameter is null, and then update
the context variables with the input string.
- In PlanTests.cs, add a new test method called
CanExecutePlanWithContextAsync that creates a mock context with some
variables, memory, skills, and log, and then invokes a plan with the
context and an input string. The test asserts that the plan returns the
input string as the result, and that the context variables are updated
with the input. The test also invokes the plan again with a different
input string and the same context, and asserts that the result and the
context variables are updated accordingly.

dotnet/src/SemanticKernel.UnitTests/Planning/PlanTests.cs

@@ -47,6 +47,42 @@ public async Task CanExecutePlanAsync()
         Assert.Equal("Some input", result.Result);
     }
 
+
+    [Fact]
+    public async Task CanExecutePlanWithContextAsync()
+    {
+        // Arrange
+        var goal = "Write a poem or joke and send it in an e-mail to Kai.";
+        var plan = new Plan(goal);
+        var kernel = new Mock<IKernel>();
+        var log = new Mock<ILogger>();
+        var memory = new Mock<ISemanticTextMemory>();
+        var skills = new Mock<ISkillCollection>();
+
+        var context = new SKContext(
+            new ContextVariables("Some input"),
+            memory.Object,
+            skills.Object,
+            log.Object
+        );
+
+        // Act
+        var result = await plan.InvokeAsync(context);
+
+        // Assert
+        Assert.NotNull(result);
+        Assert.Equal("Some input", result.Result);
+
+        plan = new Plan(goal);
+
+        // Act
+        result = await plan.InvokeAsync("other input", context);
+
+        // Assert
+        Assert.NotNull(result);
+        Assert.Equal("other input", result.Result);
+    }
+
     [Fact]
     public async Task CanExecutePlanWithPlanStepAsync()
     {

dotnet/src/SemanticKernel/Planning/Plan.cs

@@ -288,7 +288,10 @@ public FunctionView Describe()
     public Task<SKContext> InvokeAsync(string input, SKContext? context = null, CompleteRequestSettings? settings = null, ILogger? log = null,
         CancellationToken? cancel = null)
     {
-        context ??= new SKContext(new ContextVariables(input), null!, null, log ?? NullLogger.Instance, cancel ?? CancellationToken.None);
+        context ??= new SKContext(new ContextVariables(), null!, null, log ?? NullLogger.Instance, cancel ?? CancellationToken.None);
+
+        context.Variables.Update(input);
+
         return this.InvokeAsync(context, settings, log, cancel);
     }