
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
Given the origin of a Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, and adopting the same unit of length in both coordinate systems, find the shortest distance from a point on the curve $\rho^2 - 2\rho\cos\theta - 1 = 0$ to a point on the curve $\left\{ \begin{matrix} x = 3 - t \\ y = 1 + t \end{matrix} \right.$ (where $t$ is a parameter).

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