
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 $f(x)=M\sin (\omega x+\varphi)$ ($M > 0$, $\omega > 0$, $|\varphi| < \frac {\pi}{2}$), the graph intersects the $x$-axis at two adjacent points $A(0,0)$ and $B(6,0)$. Point $C$ is a highest point on the graph of $f(x)$. Let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ in $\triangle ABC$, respectively, satisfying $(a+c)(\sin C-\sin A)=(a+b)\sin B$.
- (I) Find the expression of the function $f(x)$.
- (II) After shifting the graph of the function $f(x)$ to the left by 1 unit without changing the vertical coordinates and stretching the horizontal coordinates by $\frac {\pi}{3}$ times, we get the graph of the function $g(x)$. Find the intervals where $g(x)$ is monotonically decreasing.

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