
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 circle of radius  $2$  is inscribed in equilateral triangle  $ABC$ . The altitude from  $A$  to  $BC$  intersects the circle at a point  $D$  not on  $BC$ .  $BD$  intersects the circle at a point  $E$  distinct from  $D$ . Find the length of  $BE$ .

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