
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 $r$ be a real number with $|r| < 4$, and let $z$ be a complex number satisfying the equation
\[sz + \frac{1}{z} = r,\]
where $s$ is a real number and $s \neq 0$. Find $|z|$.

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