
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 equation of circle $C$ is $\rho=2a\cos \theta (a > 0)$. Taking the pole as the origin of the coordinate system and the polar axis as the positive half-axis of the $x$-axis, we establish a plane rectangular coordinate system. Suppose the parametric equation of line $l$ is $\begin{cases} x=5t+1 \\ y=12t-1 \end{cases} (t$ is the parameter$)$, if line $l$ always has common points with circle $C$, find the range of the real number $a$.

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