
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 $g$ be a function defined by $g(x)= \frac{ax+b}{cx+d}$, where $a$, $b$, $c$, and $d$ are nonzero real numbers. Given that $g(13)=13$, $g(31)=31$, and $g(g(x))=x$ for all values except $\frac{-d}{c}$, find the unique number that is not in the range of $g$.

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