
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
There are four inequalities given below:
$\int_{0}^{1} \sqrt{x}dx < \int_{0}^{1} 3x dx$;
$\int_{0}^{\frac{\pi}{4}} \sin xdx < \int_{0}^{\frac{\pi}{4}} \cos xdx$;
$\int_{0}^{1} e^{-x}dx < \int_{0}^{1} e^{-x^{2}}dx$;
$\int_{0}^{2} \sin xdx < \int_{0}^{2} xdx$.
Determine the number of inequalities that hold true.

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