
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
Given an equilateral triangle $ABC$ with side length 11, points $A_1$, $B_1$, $C_1$ are taken on sides $BC$, $CA$, $AB$ respectively such that $AC_1 = BA_1 = CB_1 = 5$. Find the ratio of the area of triangle $ABC$ to the area of the triangle formed by the lines $A A_1$, $B B_1$, $C C_1$.

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