
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
Given a prism \(ABC-A'B'C'\) with a base that is an equilateral triangle with side length 2, the lateral edge \(AA'\) forms a 45-degree angle with the edges \(AB\) and \(AC\) of the base. Point \(A'\) is equidistant from the planes \(ABC\) and \(BB'C'C\). Find \(A'A = \_\_\_\_\_ \).

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