
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 congruent. The vertices \( A_1 \), \( B_1 \), and \( C_1 \) are located on the extensions of side \( BC \) beyond point \( C \), side \( BA \) beyond point \( A \), and side \( AC \) beyond point \( C \), respectively, such that \( B_1C_1 \perp BC \). Find angle \( B \).

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