
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  $\angle XOY = \frac{\pi}{2}$ ;  $P$  is a point inside  $\angle XOY$  and we have  $OP = 1; \angle XOP = \frac{\pi}{6}.$  A line passes  $P$  intersects the Rays  $OX$  and  $OY$  at  $M$  and  $N$ . Find the maximum value of  $OM + ON - MN.$ 

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