
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
The walls of a room are in the shape of a triangle  $ABC$  with  $\angle ABC = 90^\circ$ ,  $\angle BAC = 60^\circ$ , and  $AB=6$ .  Chong stands at the midpoint of  $BC$  and rolls a ball toward  $AB$ .  Suppose that the ball bounces off  $AB$ , then  $AC$ , then returns exactly to Chong.  Find the length of the path of the ball.

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