
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 $C$: $ρ=2a\cos θ (a > 0)$, and $l$: $ρ\cos (θ-\frac{π}{3})=\frac{3}{2}$, have exactly one common point.
(I) Find the value of $a$;
(II) Let $O$ be the pole, and $A$, $B$ be two points on $C$ such that $∠AOB=\frac{π}{3}$, find the maximum value of $|OA|+|OB|$.

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