
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 polar equation of line $l$ is $\rho\cos \left( \theta + \frac{\pi}{3} \right)=1.$ Taking the pole $O$ as the origin and the positive half-axis of the polar axis as the $x$-axis, the parametric equation of circle $C$ is $\begin{cases} x = r\cos\theta, \\ y = r\sin\theta \end{cases}$ (where $\theta$ is the parameter). If line $l$ is tangent to circle $C$, find the value of $r$.

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