
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 set of equations:
\\(S\_{1}=1\\)
\\(S\_{2}=2+3=5\\)
\\(S\_{3}=4+5+6=15\\)
\\(S\_{4}=7+8+9+10=34\\)
\\(S\_{5}=11+12+13+14+15=65\\)
\\(S\_{6}=16+17+18+19+20+21=111\\)
\\(S\_{7}=22+23+24+25+26+27+28=175\\)
\\(…\\)
Find the value of \\(S\_{1}+S\_{3}+S\_{5}+…+S\_{2n-1}=\\) \_\_\_\_\_\_ .

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