
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 an isosceles right triangle, the radius of the inscribed circle is 2.

Find the distance from the vertex of the acute angle to the point where the inscribed circle touches the leg opposite to this angle.

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