
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 right triangle with hypotenuse  $AC$ . A square is inscribed in the triangle such that points  $D,E$  are on  $AC$ ,  $F$  is on  $BC$ , and  $G$  is on  $AB$ . Given that  $AG=2$  and  $CF=5$ , what is the area of  $\triangle BFG$ ?

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