
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
What is the number of units in the area of the sector subtended by an angle of $60^\circ$ at the center of the circle with center at point $P$ and passing through point $Q$? Express your answer in terms of $\pi$.

[asy]
size(150); pair P = (2,-2), Q=(8,6); pair R=(2,6); draw(circle(P, distance(P,Q)), dashed); draw(P--Q); draw(P--R); string stringpair(pair p){return "$("+string(p.x)+", "+string(p.y)+"$)";};
dot("$P$"+stringpair(P),P,NW,linewidth(3)); dot("$Q$"+stringpair(Q),Q,NE,linewidth(3)); dot("$R$"+stringpair(R),R,N,linewidth(3));

[/asy]

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