
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 real numbers $x$, define a function:
\[ f(x) = \begin{cases} 
3x + b & \text{if } x > -2, \\
-x + 4 & \text{if } x \leq -2.
\end{cases} \]
Determine the value of $b$ for which $f(x)$ is continuous.

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