
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 $y$ be a real number. Consider the following five statements:
1. $1 < y^2 < 4$
2. $y^2 > 4$
3. $-2 < y < 0$
4. $0 < y < 2$
5. $0 < y^3 - y^2 < 4$

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

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