
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
Let \(\angle X O Y = 90^{\circ}\), \(P\) be a point inside \(\angle X O Y\) such that \(O P = 1\) and \(\angle X O P = 30^{\circ}\). Draw an arbitrary line through \(P\) intersecting rays \(OX\) and \(OY\) at points \(M\) and \(N\) respectively. Find the maximum value of \(OM + ON - MN\).

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