
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
\[ g(x) = x^3 + 4x^2 + 10x + 20. \]
The graphs of $y = g(x)$ and $y = g^{-1}(x)$ intersect at exactly one point $(a,b)$. Determine the ordered pair $(a,b)$.

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