
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
For constants $p$ and $q$, let:
\[ f(x) = \left\{
\begin{array}{cl}
px + q & \text{if } x < -1, \\
5x - 10 & \text{if } x \ge -1.
\end{array}
\right.\]
The function $f$ has the property that $f(f(x)) = x$ for all $x$. Find the values of $p + q$.

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