
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
The shortest chord length obtained by the intersection of the line $l$ with parameter $t$ and the circle $C$ with parameter $\theta$ is _______.

$$
l: 
    \begin{cases} 
        x = -1 + t\cos\alpha \\
        y = 1 + t\sin\alpha
    \end{cases}
$$

$$
C: 
    \begin{cases} 
        x = 2 + 4\cos\theta \\
        y = 1 + 4\sin\theta
    \end{cases}
$$

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