
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 $x$ be a real number. Consider the following five statements:

1. $0 < x^2 < 1$
2. $x^2 > 1$
3. $-1 < x < 0$
4. $0 < x < 1$
5. $0 < x - \sqrt{x} < 1$

What is the maximum number of these statements that can be true for any value of $x$?

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