
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
In the diagram below, $\triangle ABC$ is an isosceles triangle with $AB = AC$, and $M$ and $N$ are the midpoints of $AB$ and $AC$ respectively. It is given that $CM$ is perpendicular to $BN$, $BC = 20$ cm, and the area of $\triangle ABC$ is $x$ cm². Find the value of $x$.

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