
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
Calculate the sums:

a) \(C_{5}^{0}+2 C_{5}^{1}+2^{2} C_{5}^{2}+\ldots+2^{5} C_{5}^{5}\)

b) \(C_{n}^{0}-C_{n}^{1}+\ldots+(-1)^{n} C_{n}^{n}\)

c) \(C_{n}^{0}+C_{n}^{1}+\ldots+C_{n}^{n}\).

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