
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 quadratic function $f(x)=ax^{2}+(b-2)x+3$, and $-1$, $3$ are the roots of the function $f(x)$.

(Ⅰ) Find the expression for $f(x)$ and solve the inequality $f(x) \leqslant 3$;

(Ⅱ) If $g(x)=f(\sin x)$, find the range of the function $g(x)$.

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