
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
Let \\(\{a_n\}\) be a geometric sequence with a positive common ratio, where \\(a_1=2, a_3=a_2+4\\).

\\((1)\\) Find the general formula for \\(\{a_n\}\).

\\((2)\\) Calculate the sum of the first \\(n\\) terms, \\(S_n\\), of the sequence \\(\{(2n+1)a_n\}\).

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