
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 \( a \) and \( b \), consider the function \( f \) defined by
\[
f(x) = \left\{
\begin{array}{cl}
ax^2 + b & \text{if } x < 3, \\
10 - 2x & \text{if } x \ge 3.
\end{array}
\right.
\]
The function \( f \) has the property that \( f(f(x)) = x \) for all \( x \). Determine the values of \( a \) and \( b \).

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