
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 that the maximum value of the function f(x) = A sin(2x + φ) (where A > 0, |φ| ∈ (0, $\frac{π}{2}$)) is $\sqrt{2}$, and the graph passes through the point ($\frac{π}{3}$, $\frac{\sqrt{6}}{2}$).

1. Find the analytical expression of f(x);
2. Find the maximum and minimum values of f(x) when x ∈ [$\frac{π}{6}$, $\frac{π}{2}$].

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