
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 following four inequalities:
1. $a^2 + b^2 + c^2 \geq ab + bc + ac$
2. $a(1-a) \leq \frac{1}{4}$
3. $\frac{a}{b} + \frac{b}{a} \geq 2$
4. $(a^2 + b^2)(c^2 + d^2) \geq (ac + bd)^2$

Determine which of the above inequalities always hold true.

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