
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 point $P$ is chosen inside $\triangle ABC$ such that lines drawn through $P$ parallel to $\triangle ABC$'s sides create three smaller triangles \( t'_{1}, t'_{2}, t'_{3} \) with areas \( 16, 25, \) and \( 64 \) respectively. Determine the area of $\triangle ABC$.

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