
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 the function $f(x)=\sin^2 \omega x - \cos^2 \omega x + 2\sqrt{3}\sin \omega x \cdot \cos \omega x + \lambda$ have its graph symmetric about the line $x=\pi$, where $\omega$ and $\lambda$ are constants, and $\omega \in \left( \frac{1}{2}, 1 \right)$.

(Ⅰ) Find the smallest positive period of the function $f(x)$;

(Ⅱ) If the graph of $y=f(x)$ passes through the point $\left( \frac{\pi}{4}, 0 \right)$, find the range of values of the function $f(x)$ in the interval $\left[0, \frac{3\pi}{5} \right]$.

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