
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
In an isosceles triangle \( ABC \) (\(AB = BC\)), the altitudes \( AA_1 \), \( BB_1 \), and \( CC_1 \) are drawn.

Find the ratio of the area of triangle \( A_1B_1C_1 \) to the area of triangle \( ABC \), given that \( \frac{AB}{A_1B_1} = \sqrt{3} \).

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