
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
Compute the integrals:
1) \(\int_{0}^{5} \frac{x \, dx}{\sqrt{1+3x}}\)
2) \(\int_{\ln 2}^{\ln 9} \frac{dx}{e^{x}-e^{-x}}\)
3) \(\int_{1}^{\sqrt{3}} \frac{(x^{3}+1) \, dx}{x^{2} \sqrt{4-x^{2}}}\)
4) \(\int_{0}^{\frac{\pi}{2}} \frac{dx}{2+\cos x}\)

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