
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
Determine how many real numbers $z$ satisfy the equation 
\[
  e^{2z} = \frac{z - 2}{z + 2}
\]
given that $-10 \leq z \leq 10$.

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