
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 a Cartesian coordinate system, the parametric equation of line $l$ is $\begin{cases} x=t \\ y= \sqrt{3}t+2\end{cases}$ (where $t$ is the parameter), and the parametric equation of circle $C$ is $\begin{cases} x=a\cos \theta \\ y=a\sin \theta \end{cases}$ (where $a > 0$ and $\theta$ is the parameter). Let point $P$ be any point on circle $C$. If the maximum distance from point $P$ to line $l$ is $3$, find the value of $a$.

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