
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: $1 \cdot 2 \cdot 3 \cdot 4 + 1 = 5^2$,  
$2 \cdot 3 \cdot 4 \cdot 5 + 1 = 11^2$,  
$3 \cdot 4 \cdot 5 \cdot 6 + 1 = 19^2$,  
...  
(1) Please state a general conclusion and provide a proof;  
(2) Based on (1), calculate the result of $2000 \cdot 2001 \cdot 2002 \cdot 2003 + 1$ (express the result in the simplest form).

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