
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
For how many odd integers k between 0 and 100 does the equation 2^(4 m^(2) )+2^(m^(2)-n^(2)+4)=2^(k+4)+2^(3 m^(2)+n^(2)+k) have exactly two pairs of positive integers (m, n) that are solutions?

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