
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. \( 0 < y^3 < 1 \)
2. \( y^3 > 1 \)
3. \( -1 < y < 0 \)
4. \( 0 < y < 1 \)
5. \( 0 < y^2 - y^3 < 1 \)

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