
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 general solution of the first-order differential inequality \( y' + p(x)y \geq q(x) \) is \( x = e^{-\int \rho(x) dr} \left[ \int q(x) e^{\int(x) \, d} dx + \int g(x) dx \right] \), \( \forall g(x) \geq 0 \). The equality holds if and only if \( g(x) = 0 \).

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