
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 the natural number $m$ which is greater than or equal to 2, the $n$-th power of $m$ can be decomposed as follows:

$$2^2 = 1 + 3,\\
3^2 = 1 + 3 + 5,\\
4^2 = 1 + 3 + 5 + 7,$$

$$2^3 = 3 + 5,\\
3^3 = 7 + 9 + 11,\\
4^3 = 13 + 15 + 17 + 19.$$

According to the decomposition pattern above, then $5^2 =$ _______;

If the smallest number in the decomposition of $m^3$ (where $m \in \mathbb{N^*}$) is 21, the value of $m$ is _______.

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