
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 triangle \( ABC \), angle \( B \) is a right angle, and the measure of angle \( A \) is \( \alpha \) \((\alpha < 45^\circ)\). Point \( D \) is the midpoint of the hypotenuse. Point \( C_1 \) is symmetric to point \( C \) with respect to line \( BD \). Find angle \( AC_1B \).

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