
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 equation of curve $C$ as $ \begin{cases} x=a+4\cos \theta \ y=1+4\sin \theta \end{cases} (\theta \text{ is the parameter, } a > 0 )$, and the polar coordinate equation of line $l$ as $3\rho\cos \theta+4\rho\sin \theta=5$, if curve $C$ and line $l$ have only one common point, then the value of real number $a$ is _____ .

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