
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
If $$S_{1} = \int_{0}^{\frac{\pi}{2}} \cos x dx$$, $$S_{2} = \int_{1}^{2} \frac{1}{x} dx$$, and $$S_{3} = \int_{1}^{2} e^{x} dx$$, determine the relationship among $S_{1}$, $S_{2}$, and $S_{3}$.

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