
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
If \( z_{1}, z_{2}, \cdots, z_{n} \in \mathbf{C}, \left|z_{1}\right|=\left|z_{2}\right|=\cdots=\left|z_{n}\right|=r \neq 0, \) and \( T_{s} \) represents the sum of all possible products of \( s \) out of these \( n \) numbers, find \( \left|\frac{T_{s}}{T_{n-s}}\right| \) in terms of \( r \) given that \( T_{n-s} \neq 0 \).

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