
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 power of $n$ of a natural number $m$ greater than or equal to 2, there are the following decomposition methods:
$$2^2 = 1 + 3$$
$$3^2 = 1 + 3 + 5$$
$$4^2 = 1 + 3 + 5 + 7$$
$$2^3 = 3 + 5$$
$$3^3 = 7 + 9 + 11$$
$$4^3 = 13 + 15 + 17 + 19$$
According to the above decomposition rule, then $5^2 = 1 + 3 + 5 + 7 + 9$, if the smallest number in the decomposition of $m^3$ ($m \in \mathbb{N}^*$) is 73, then the value of $m$ is ___.

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