
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
Consider the function $f$ defined by $f(x) = \frac{ax+b}{cx+d}$, where $a, b, c, d$ are nonzero real numbers. The function has properties $f(10) = 10$, $f(50) = 50$ and $f(f(x)) = x$ for all values except $\frac{-d}{c}$. 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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