
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
Given an angle of $30^{\circ}$. Construct a circle with a radius of 2.5, that is tangent to one side of the angle and has its center on the other side. Find the distance from the center of the circle to the vertex of the angle.

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