
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
A square \(ABCD\) has a side length of 40 units. Point \(F\) is the midpoint of side \(AD\). Point \(G\) lies on \(CF\) such that \(3CG = 2GF\). What is the area of triangle \(BCG\)?

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