
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
\[g(x) = \left\{
\begin{array}{cl}
x + 5 & \text{if $x < 15$}, \\
3x - 1 & \text{if $x \ge 15$}.
\end{array}
\right.\]
Find $g^{-1}(10) + g^{-1}(50)$.

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