
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 $S_{1}= \int_{1}^{2} x dx$, $S_{2}= \int_{1}^{2} e^{x} dx$, and $S_{3}= \int_{1}^{2} x^{2} dx$, determine the relation in size among $S_{1}$, $S_{2}$, and $S_{3}$.

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