
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 given triangle \( \triangle ABC \) with an area of 36, point \( D \) is on \( AB \) such that \( BD = 2AD \), and point \( E \) is on \( DC \) such that \( DE = 2EC \). What is the area of \( \triangle BEC \)?

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