
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  
\\( C_{ 5 }^{ 1 }+ C_{ 5 }^{ 5 }=2^{3}-2\\)  
\\( C_{ 9 }^{ 1 }+ C_{ 9 }^{ 5 }+ C_{ 9 }^{ 9 }=2^{7}-2^{3}\\)  
\\( C_{ 13 }^{ 1 }+ C_{ 13 }^{ 5 }+ C_{ 13 }^{ 9 }+ C_{ 13 }^{ 13 }=2^{11}-2^{5}\\)  
\\( C_{ 17 }^{ 1 }+ C_{ 17 }^{ 5 }+ C_{ 17 }^{ 9 }+ C_{ 17 }^{ 13 }+ C_{ 17 }^{ 17 }=2^{15}-2^{7}\\)  
\\(…\\)  
Following the pattern above, then \\( C_{ 4n+1 }^{ 1 }+ C_{ 4n+1 }^{ 5 }+…+ C_{ 4n+1 }^{ 4n+1 }=\\) ______.

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