
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
Given the parametric equations of the curve $C$ as $ \begin{cases} x=a+4\cos θ \\\\ y=1+4\sin θ\end{cases} (θ \text{ is a parameter}, a > 0)$, and the polar coordinate equation of the line $l$ as $3ρ\cos θ+4ρ\sin θ=5$, find the value of the real number $a$ such that the curve $C$ and the line $l$ have only one common point.

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