
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
1. In the polar coordinate system, it is known that the circle $\rho=2\cos\theta$ is tangent to the line $3\rho\cos\theta+4\rho\sin\theta+a=0$. Find the value of the real number $a$.
2. In the polar coordinate system, find the distance from point $P(2, \frac {11\pi}{6})$ to the line $\rho\sin(\theta- \frac {\pi}{6})=1$.

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