
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given that the side length of square $ABCD$ is 1, point $M$ is the midpoint of side $AD$, and with $M$ as the center and $AD$ as the diameter, a circle $\Gamma$ is drawn. Point $E$ is on segment $AB$, and line $CE$ is tangent to circle $\Gamma$. Find the area of $\triangle CBE$.

Present the answer in LaTex format: \boxed{Your answer}
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