
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 of the function intersects the x-axis at two adjacent points A(0,0) and B(6,0), and C is a maximum point of the function $f(x)$. 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 $f(x)$ 1 unit to the left without changing the y-coordinate and stretching the x-coordinate by a factor of $\frac{\pi}{3}$, obtain 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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