
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
Let  $\triangle ABC$  be a triangle with  $AB=5, BC=6, CA=7$ . Suppose  $P$  is a point inside  $\triangle ABC$  such that  $\triangle BPA\sim \triangle APC$ . If  $AP$  intersects  $BC$  at  $X$ , find  $\frac{BX}{CX}$ .

[i]Proposed by Nathan Ramesh

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