
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
A prime number  $p$  is a **moderate** number if for every  $2$  positive integers  $k > 1$  and  $m$ , there exists k positive integers  $n_1, n_2, ..., n_k $  such that \[ n_1^2+n_2^2+ ... +n_k^2=p^{k+m} \]
If  $q$  is the smallest **moderate** number, then determine the smallest prime  $r$  which is not moderate and  $q < r$ .

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