
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) = 2sin(ωx + φ) (ω > 0, |φ| < $\frac{π}{2}$), the distance between two adjacent symmetry axes of the graph is $\frac{π}{2}$. After shifting the graph of function f(x) to the left by $\frac{π}{3}$ units, we obtain the graph of function g(x). If function g(x) is an even function, find the range of function f(x) in the interval [-$\frac{π}{6}$, $\frac{π}{6}$].

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