
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
There is a point in a plane around which three rays extend, creating three angles. Two of the angles are equal, and the sum of these two equal angles is four times the third angle. If one of the equal angles is $x^\circ$, and the third angle is $30^\circ$ less than one of the equal angles, find $x$.

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