
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
Given the function $f(x) = \sin\left(2x + \frac{π}{6}\right)$, where $x \in \left[-\frac{π}{6}, α\right]$. When $a = \frac{π}{3}$, the range of $f(x)$ is \_\_\_\_\_\_\_\_; When the range of $f(x)$ is $\left[- \frac{1}{2}, 1\right]$, the range of $a$ is \_\_\_\_\_\_\_\_.

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