
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
Find the length of the diagonal of a square, two vertices of which lie on the circle of radius \( R \), and the other two vertices lie on the tangent to this circle.

Given: \(\omega(0,|OA|)\) is the circle, \(|OA|=R\), \(ABCD\) is the square, \(A \in \omega\), \(D \in \omega\), \((BC)\) is tangent to \(\omega\), \([AC]\) is the diagonal of the square.

Find: \(|AC|\).

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