
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
Express the following expressions in terms of elementary symmetric polynomials:
a) \((x+y)(y+z)(x+z)\)

b) \(x^{3} + y^{3} + z^{3} - 3xyz\)

c) \(x^{3} + y^{3}\)

d) \(\left(x^{2}+y^{2}\right)\left(y^{2}+z^{2}\right)\left(x^{2}+z^{2}\right)\)

e) \(x_{1}^{2} + x_{2}^{2} + \ldots + x_{n}^{2}\)

f) \(x^{4} + y^{4} + z^{4}\)

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