
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 a triangle with side lengths of 2, 3, and 4, the angle bisector of the largest angle divides the original triangle into two smaller triangles. Find the ratio of the areas of the smaller triangle to that of the larger triangle.

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