
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 \(\triangle ABC\), \(\angle BAC = 45^\circ\). \(D\) is a point on \(BC\) such that \(AD\) is perpendicular to \(BC\). If \(BD = 3 \, \text{cm}\) and \(DC = 2 \, \text{cm}\), and the area of \(\triangle ABC\) is \(x \, \text{cm}^2\), find the value of \(x\).

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