
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 fly is sitting at vertex $A$ of a triangular room $ABC$ $\left(\angle B=60^\circ, \angle C=45^\circ, AB=5 \text{ meters}\right)$. At some point, it flies off in a random straight-line direction. Each time it hits a wall, it turns $60^\circ$ and continues flying in a straight line. Can it happen that after some time the fly will have flown more than 12 meters?

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