
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: ①$1+6\times 1=4^{2}-9\times 1^{2}$; ②$1+6\times 2=7^{2}-9\times 2^{2}$; ③$1+6\times 3=10^{2}-9\times 3^{2}$; $\ldots \ldots $ According to the above pattern, write down the $n$-th equation you guess ______.

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