
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 circle of radius 1. From an external point $M$, two mutually perpendicular tangents $MA$ and $MB$ are drawn to the circle. A random point $C$ is chosen on the smaller arc $AB$ between the tangent points $A$ and $B$, and a third tangent $KL$ is drawn through this point. This forms a triangle $KLM$ with the tangents $MA$ and $MB$. Find the perimeter of this triangle.

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