
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 $A(2,0)$ be a fixed point in the plane, and let $P\left(\sin \left(2 t-60^{\circ}\right), \cos \left(2 t-60^{\circ}\right)\right)$ be a moving point. Find the area swept by the line segment $AP$ as $t$ changes from $15^{\circ}$ to $45^{\circ}$.

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