
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 $m$ and $n$ be two odd integers such that $m = 2a + 3$ and $n = 2b + 1$, and $n < m$. Determine the largest integer that divides all possible numbers of the form $m^2 - n^2$, where $a$ and $b$ are integers.

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