
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 $f(x)=M\sin (ωx+φ)(M > 0,|φ| < \dfrac {π}{2},0 < ω < 3)$, one of the highest points on the graph is $(\dfrac {2}{3}π,2)$, and the graph of the function $f(x)$ intersects the $y$-axis at $(0,1)$.
(I) Find the values of $M$, $ω$, and $φ$;
(II) In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and satisfy $(2a-c)\cos B=b\cos C$. Find the range of values for the function $f(A)$.

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