
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 \[f(x) =
\begin{cases}
3x^2 + 1 &\text{if } x \leq 3, \\
bx - 6 &\text{if } x > 3.
\end{cases}
\]
Find \( b \) such that the graph of \( y = f(x) \) is continuous at \( x = 3 \).

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