
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
Observe the following equations: $2^{3}=3+5$, $3^{3}=7+9+11$, $4^{3}=13+15+17+19$, $5^{3}=21+23+25+27+29$, $(\ldots)$, if the method similar to the above equations is used to decompose $m^{3}$ and the last number on the right side of the equation is $109$, then the positive integer $m$ equals \_\_\_\_\_\_.

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