
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 quintuples $(x_1, x_2, x_3, x_4, x_5)$ of positive odd integers that satisfy $\sum_{i = 1}^5 x_i = 100$. Find $\frac{n}{100}$.

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