
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 $f(x)=2\sin ωx (0 < ω < 3)$ with a minimum value of $- \sqrt {3}$ on $\[- \frac {π}{6},0\]$ and a graph that, when all points are shifted right by $\frac {π}{3}$ units, results in the graph of function $g(x)$.
(I) Find the analytical expression of function $g(x)$;
(II) In $\triangle ABC$, angles $A$, $B$, and $C$ correspond to edges $a$, $b$, and $c$, respectively. If the first zero point of function $g(x)$ on the right side of the y-axis is exactly $A$ and $a=5$, find the maximum value of the area $S$ of $\triangle ABC$.

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