
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
Given the equations: 

$49 = 7^{2}$,  
$4489 = 67^{2}$,  
$444889 = 667^{2}$,  
...

Is it possible that 

$\underbrace{444 \cdots}_{n+1} \underbrace{488 \cdots 89}_{n} = \underbrace{66 \cdots 67^{2}}_{n} \quad (n \in \mathbf{N})$ ?

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