
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. Three lines divide the triangle into four triangles and three pentagons. One of the triangles has its three sides along the new lines, while the other three triangles each have two sides along the new lines. If all four triangles are congruent, find the area of each in terms of the area of triangle ABC.

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