
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
Determine the least odd number  $a > 5$  satisfying the following conditions: There are positive integers  $m_1,m_2, n_1, n_2$  such that  $a=m_1^2+n_1^2$ ,  $a^2=m_2^2+n_2^2$ , and  $m_1-n_1=m_2-n_2.$ 

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