
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:
$$
\left(10^{4}-9^{4}+8^{4}-7^{4}+\cdots+2^{4}-1^{4}\right)+\left(10^{2}+9^{2}+5 \times 8^{2}+5 \times 7^{2}+9 \times 6^{2}+9 \times 5^{2}+13 \times 4^{2}+13 \times 3^{2}\right)
$$

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