
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 curve $y = x^3 + x - 2$, its tangent line ${l_1}$ at point $P_0$ is parallel to the line $4x - y - 1 = 0$, and point $P_0$ is in the third quadrant.

(1) Find the coordinates of point $P_0$;
(2) If line $l \perp {l_1}$, and line $l$ also passes through the tangent point $P_0$, find the equation of line $l$.

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