
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
Given the following equations: \\((1)2^{2}-1^{2}=3\\)；\\((2)3^{2}-2^{2}=5\\)；\\((3)4^{2}-3^{2}=7\\)，\\(…\\)
(1) Please observe carefully and write out the fourth equation;
(2) Please find the pattern and write out the nth equation;
(3) Using the pattern found in (2), calculate: \\(1+3+5+7+…+2005+2007\\).

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