
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]


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For natural numbers greater than or equal to $2$, the following decompositions are given:  
$2^{2}=1+3$  
$3^{2}=1+3+5$  
$4^{2}=1+3+5+7$  
$2^{3}=3+5$  
$3^{3}=7+9+11$  
$4^{3}=13+15+17+19$  
Based on the above decomposition rules, if $n^{2}=1+3+5+…+19$ and the smallest number in the decomposition of $m^{3}$ is $43$, then $m+n=$ \_\_\_\_\_\_.

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