
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

Consider the real numbers \(a\) and \(b\) such that \(a^3 - b^3 = 2\) and \(a^5 - b^5 \geq 4\).

(a) Knowing that for any real \(x\) and \(y\), \(x^3 - y^3 = (x - y)(x^2 + xy + y^2)\), verify that \(a > b\).

(b) Verify that \(a^2 + b^2 \geq 2\).

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