
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 polar equation of the curve $C_1$ is $\rho\cos^2\theta=\sin\theta$, and the parametric equation of the curve $C_2$ is 
$$
\begin{cases}
x=3-t \\
y=1-t
\end{cases}
$$
With the pole as the origin and the polar axis as the positive $x$-axis, establish a Cartesian coordinate system, then the shortest distance between a point on curve $C_1$ and a point on curve $C_2$ is ______.

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