
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
\(ABC\) is a triangle such that \(BC = 10\), \(CA = 12\). Let \(M\) be the midpoint of side \(AC\). Given that \(BM\) is parallel to the external bisector of \(\angle A\), find the area of triangle \(ABC\). (Lines \(AB\) and \(AC\) form two angles, one of which is \(\angle BAC\). The external bisector of \(\angle A\) is the line that bisects the other angle.)

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