
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
A function \( f \) is defined by \( f(z) = -i\overline{z} \), where \( i^2 = -1 \) and \( \overline{z} \) is the complex conjugate of \( z \). Determine how many values of \( z \) satisfy both \( |z| = 7 \) and \( f(z) = z \).

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