
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 is $$\begin{cases} \left.\begin{matrix}x=a+4\cos\theta \\ y=1+4\sin\theta\end{matrix}\right.\end{cases}, (\theta \text{ is the parameter, } a>0),$$ if curve C intersects with the line $3x+4y-5=0$ at only one point, then the value of the real number $a$ is \_\_\_\_\_\_.

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