
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 the regular triangular prism \(A B C A_1 B_1 C_1\) (\(A A_1 \| B B_1 \| C C_1\)), the angle between the lines \(A C_1\) and \(A_1 B\) is \(\alpha\). Given \(A A_1 = 2\), find \(A B\).

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