
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 powers of natural numbers greater than or equal to 2, the following decompositions apply:  
$2^2 = 1 + 3$,  
$3^2 = 1 + 3 + 5$,  
$4^2 = 1 + 3 + 5 + 7$,  
$2^3 = 3 + 5$,  
$3^3 = 7 + 9 + 11$,  
$4^3 = 13 + 15 + 17 + 19$.  
According to the above pattern of decomposition, what is the sum for $5^2$? If the smallest number in the decomposition of $m^3$ (where $m \in \mathbb{N}^*$) is 21, what is the value of m?

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