
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
Isosceles triangles \(ABC (AB = BC)\) and \(A_1B_1C_1 (A_1B_1 = B_1C_1)\) are similar and \(AB : A_1B_1 = 2 : 1\).

Vertices \(A_1, B_1\), and \(C_1\) are located on sides \(CA, AB,\) and \(BC\) respectively, with \(A_1B_1 \perp AC\). Find angle \(B\).

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