
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 function $f(x) = 2\sin{ωx}\cos{ωx} + 2\sqrt{3}\sin^2{ωx} - \sqrt{3} (ω > 0)$ has a minimum positive period of $π$.
1. Find the value of $ω$ and the interval where the function $f(x)$ is monotonically decreasing.
2. The graph of the function $f(x)$ is shifted to the left by $\frac{π}{6}$ units and then upward by 1 unit to obtain the graph of the function $y = g(x)$. If the function $y = g(x)$ has at least 10 zeros on the interval $[0, b] (b > 0)$, find the minimum value of $b$.

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