
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 $n$ be the number of ordered quadruples $(x_1, x_2, x_3, x_4)$ of integers such that $x_1$ is a squared odd integer minus 1 and $x_2, x_3, x_4$ are positive odd integers which satisfy $\sum_{i=1}^4 x_i = 100$. Find $n$.

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