
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 Cartesian coordinate system $xoy$, with the origin as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The length of the chord that the line
$$
\begin{cases}
x = -2 + t \\
y = 1 - t
\end{cases}
(t \text{ is the parameter})
$$
intersects with the circle $\rho^2 + 2\rho\cos\theta - 3 = 0$ is \_\_\_\_\_\_\_\_\_\_\_\_\_.

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