
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
Construct the tangents $l_1$ and $l_2$ from a point $P$ on the line $l: y = 2x$ to the circle $C: (x - 6)^2 + (y - 2)^2 = 5$, with $A$ and $B$ as the points of tangency. If $l_1$ and $l_2$ are symmetric with respect to the line $l$, then find the measure of $\angle APB$.

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