
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 point $P(3,1)$, line $l$ passing through $P$ intersects circle $C$: $(x-2)^{2}+(y-2)^{2}=4$ at points $A$ and $B$. When the length of chord $AB$ is at its minimum, the angle of inclination of line $l$ is equal to \_\_\_\_\_\_.

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