
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
Calculate: \(\frac{1^{2}+2^{2}}{1 \times 2}+\frac{2^{2}+3^{2}}{2 \times 3}+\frac{3^{2}+4^{2}}{3 \times 4}+\cdots+\frac{2005^{2}+2006^{2}}{2005 \times 2006}\)

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