
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 isosceles triangles \(ABC \quad (AB=BC)\) and \(A_{1}B_{1}C_{1} \quad (A_{1}B_{1}=B_{1}C_{1})\), the triangles are similar and \(BC : B_{1}C_{1} = 4 : 3\).

Vertex \(B_{1}\) is located on side \(AC\), vertices \(A_{1}\) and \(C_{1}\) are respectively on the extensions of side \(BA\) beyond point \(A\) and side \(CB\) beyond point \(B\), and \(A_{1}C_{1} \perp BC\). Find angle \(B\).

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