
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
Find all integers \( z \) for which exactly two of the following five statements are true, and three are false:

1) \( 2z > 130 \)
2) \( z < 200 \)
3) \( 3z > 50 \)
4) \( z > 205 \)
5) \( z > 15 \)

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