
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
In the polar coordinate system, the line $\rho\cos \theta+ \sqrt{3}\rho\sin \theta+1=0$ is tangent to the circle $\rho=2a\cos \theta (a > 0)$. Find the value of $a$.

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