
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
There are 88 numbers \( a_{1}, a_{2}, a_{3}, \ldots, a_{88} \) and each of them is either equal to -3 or -1. Given that \( a_{1}^{2} + a_{2}^{2} + \ldots + a_{88}^{2} = 280 \), find the value of \( a_{1}^{4} + a_{2}^{4} + \ldots + a_{88}^{4} \).

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