
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 triangle $ABC$, the lengths of sides $AC$ and $BC$ are fixed, while the angle at vertex $C$ varies. The midpoint of side $AC$ is $M$, the midpoint of side $BC$ is $N$, and the center of the square constructed outward on side $AB$ is $O$. How should the angle $ACB$ be chosen so that the sum of the distances $OM$ and $ON$ is maximized?

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