
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
Compute the value of
\[\sum_{i=0}^{2026} \frac{i^2}{9+i^4} \pmod{2027},\]
where  $\frac{1}{a}$  denotes the multiplicative inverse of  $a$  modulo  $2027$ .

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