
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
The function $f$ defined by $f(x)= \frac{ax+b}{cx+d}$, where $a$, $b$, $c$ and $d$ are nonzero real numbers, has the properties $f(20)=20$, $f(100)=100$, $f(f(x))=x$ for all values except $\frac{-d}{c}$, and $f'(20) = -1$. Find the unique number that is not in the range of $f$.

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