
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
Find the following integrals and verify the results by differentiation:
1) \(\int \frac{dx}{x^3}\)
2) \(\int \frac{dx}{\sqrt{2 - x^2}}\)
3) \(\int 3^t 5^t \, dt\)
4) \(\int \sqrt{y+1} \, dy\)
5) \(\int \frac{dx}{2x^2 - 6}\)

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