
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 \[f(x) =
\begin{cases}
2x^2 + 5 & \text{if } x \leq 4, \\
bx + 3 & \text{if } 4 < x \leq 6, \\
cx^2 - 2x + 9 & \text{if } x > 6.
\end{cases}
\]
Find values of $b$ and $c$ such that the graph of $y = f(x)$ is continuous.

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