
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 curve $C$: $\rho$=$(4a\cos \theta)$ ($a > 0$), and the line $l$: $\rho\cos \left(\begin{matrix} \begin{matrix}\theta- \frac{\pi}{3} \end{matrix}\end{matrix}\right)=4$, have exactly one common point.

(1) Find $a$;

(2) $O$ is the pole, $A$ and $B$ are two points on the curve $C$, and $\angle AOB = \frac{\pi}{3}$, find the maximum value of $|OA|+|OB|$.

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