
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

Demonstrate the correctness of the following identities:

(a) \((x+y)^{3}-x^{3}-y^{3}=3xy(x+y)\),

(b) \((x+y)^{5}-x^{5}-y^{5}=5xy(x+y)\left(x^{2}+xy+y^{2}\right)\),

(c) \((x+y)^{7}-x^{7}-y^{7}=7xy(x+y)\left(x^{2}+xy+y^{2}\right)^{2}\).

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