
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  $ABC$  be a triangle with circumcenter  $O$  such that  $AC = 7$ . Suppose that the circumcircle of  $AOC$  is tangent to  $BC$  at  $C$  and intersects the line  $AB$  at  $A$  and  $F$ . Let  $FO$  intersect  $BC$  at  $E$ . Compute  $BE$ .

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