
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 circle $C: x^{2}+y^{2}=16$, and line $l$ passes through point $P(2,2)$ with an inclination angle $\alpha= \dfrac{\pi}{3}$. Line $l$ intersects circle $C$ at points $A$ and $B$. Calculate the value of $|PA|\cdot|PB|$.

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