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

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}
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