
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
Let the line $l$ be defined by the parametric equations $$\begin{cases} \left.\begin{matrix}x=1+t \\ y=1+k\cdot t\end{matrix}\right.\end{cases}$$ (where $t$ is the parameter). Establish a polar coordinate system with the origin as the pole and the non-negative half of the x-axis as the polar axis. For the circle $C: \rho=2\cos\theta+4\sin\theta$, the shortest chord length where line $l$ intersects circle $C$ is \_\_\_\_\_\_.

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