
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
Inside a right angle with vertex \(O\), there is a triangle \(OAB\) with a right angle at \(A\). The height of the triangle \(OAB\), dropped to the hypotenuse, is extended past point \(A\) to intersect with the side of the angle at point \(M\). The distances from points \(M\) and \(B\) to the other side of the angle are \(2\) and \(1\) respectively. Find \(OA\).

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