
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 $f'(x) > 0$ within the interval $(a, b)$ and $f(a) \geq 0$, determine the sign of $f(x)$ within $(a, b)$.

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