
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
Let  $\ell$  be a real number satisfying the equation  $\tfrac{(1+\ell)^2}{1+\ell^2}=\tfrac{13}{37}$ .  Then
\[\frac{(1+\ell)^3}{1+\ell^3}=\frac mn,\] where  $m$  and  $n$  are positive coprime integers.  Find  $m+n$ .

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