
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
a) Determine, without using a calculator, the value of \(\sqrt{1001 \cdot 1003+1}\).

b) Verify that \((n(n+3)+1)^{2}=n(n+1)(n+2)(n+3)+1\).

c) Determine, without using a calculator, the value of \(\sqrt{(2014)(2015)(2016)(2017)+1}\).

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