
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  $\displaystyle f(x)= \frac{ax+b}{cx+d}$ . where  $a,b,c$  and  $d$  are nonzero real numbers, has the properties  $f(19)=19, f(97)=97$  and  $f(f(x))=x$  for all values except  $\displaystyle \frac{-d}{c}$ . Find the unique number that is not in the range of  $f$ .

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