
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 \[f(x) =
\begin{cases}
2x^3 - x - 2 & \text{if } x \leq 3, \\
ax + 7 & \text{if } x > 3.
\end{cases}
\]
Determine the value of \(a\) if the function \(f(x)\) is continuous at \(x = 3\).

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