
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 an isosceles right triangle \(ABC\) with a right angle at \(A\), there is a square \(KLMN\) positioned such that points \(K, L, N\) lie on the sides \(AB, BC, AC\) respectively, and point \(M\) is located inside the triangle \(ABC\).

Find the length of segment \(AC\), given that \(AK = 7\) and \(AN = 3\).

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