
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
If from any point \( P \) in the plane of triangle \( ABC \) we draw parallels to the sides of the triangle, which intersect the sides at points \( A_1, A_2, B_1, B_2, C_1, \) and \( C_2 \), then

\[
\frac{A_1A_2}{BC} + \frac{B_1B_2}{AC} + \frac{C_1C_2}{AB} = 2
\]

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