
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]


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The extensions of the medians \( AE \) and \( BF \) of an isosceles triangle \( ABC \) with base \( AB \) intersect the circumcircle at points \( A_1 \) and \( B_1 \). Find the cosine of angle \( C \) if \( A_1 B_1 = 1.5 AB \).

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