
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
In a math comprehensive and practical class, the teacher provided a set of equations: $1\times 2\times 3\times 4+1=(1^{2}+3\times 1+1)^{2}$, $2\times 3\times 4\times 5+1=(2^{2}+3\times 2+1)^{2}$, $3\times 4\times 5\times 6+1=(3^{2}+3\times 3+1)^{2}$, $\ldots$ Based on your observation, then $n\times \left(n+1\right)\times \left(n+2\right)\times \left(n+3\right)+1=$____.

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