
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) = sin²(ωx) - cos²(ωx) + 2$\sqrt {3}$sin(ωx)cos(ωx) + λ, where ω and λ are constants, and ω ∈ ($\frac{1}{2}$, 1). The graph of the function is symmetric about the line x = π.
(I) Find the smallest positive period of function f(x).
(II) If the graph of y = f(x) passes through the point ($\frac{π}{4}$, 0), find the range of f(x) in the interval [0, $\frac{3π}{5}$].

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