
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
Describe all positive integer solutions $(m, n)$ of the equation $8m - 7 = n^2$ and provide the first value of $m$ (if it exists) greater than 1959.

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