
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
Observe 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\\),  
\\(\ldots\\)  
Based on the equations above, guess that \\(S_{2n-1}=(2n-1)(an^{2}+bn+c)\\), then \\(a\cdot b\cdot c=\\) \_\_\_\_\_\_.

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