
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 that \\(\{a_n\}\) is a geometric sequence, \\(a_n > 0\), \\(a_3=12\), and \\(a_2\), \\(a_4\), \\(a_2+36\) form an arithmetic sequence.  
\\((1)\\) Find the general formula for the sequence \\(\{a_n\}\);  
\\((2)\\) Let \\(\{b_n\}\) be an arithmetic sequence, and \\(b_3=a_3\), \\(b_9=a_5\), find the sum of \\(b_3+b_5+b_7+…+b_{2n+1}\).

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