
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 equation of the line $l$ is $y=x+1$, with the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of the curve $C$ is $\rho \sin^2\theta - 4\cos \theta = 0 (\rho \geqslant 0, 0 \leqslant \theta < 2\pi)$. Find the polar radius $\rho$ of the intersection point(s) between the line $l$ and the curve $C$.

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