
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
Please observe the formula:  
1×2×3×4+1=5<sup>2</sup>  
2×3×4×5+1=11<sup>2</sup>  
3×4×5×6+1=19<sup>2</sup>  
…  
(1) Guess what is 20000×20001×20002×20003+1 equal to in the form of     <sup>2</sup>  
(2) Please state a general conclusion and provide a proof.

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