
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 rectangle  $ABEF$  is drawn on the leg  $AB$  of a right triangle  $ABC$ , whose apex  $F$  is on the leg  $AC$ . Let  $X$  be the intersection of the diagonal of the rectangle  $AE$  and the hypotenuse  $BC$  of the triangle. In what ratio does point  $X$  divide the hypotenuse  $BC$  if it is known that  $| AC | = 3 | AB |$  and  $| AF | = 2 | AB |$ ?

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