
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
Let

$$
R=3 \times 9+4 \times 10+5 \times 11+\cdots+2003 \times 2009
$$

$$
S=1 \times 11+2 \times 12+3 \times 13+\cdots+2001 \times 2011
$$

(a) Which number is larger: $\mathrm{R}$ or $S$?

(b) Calculate the difference between the larger and the smaller number.

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