
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
Let $a$ and $b$ be positive real numbers such that $a > b$. Consider the following five statements:
1. $\frac{1}{a} > \frac{1}{b}$
2. $a^2 > b^2$
3. $a > b$
4. $|a| > 1$
5. $b < 1$

What is the maximum number of these statements that can be true for any values of $a$ and $b$?

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