
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 $f(x)=ax^2+bx+c (a\neq 0)$, it is known that $f(0)=2$ and $f(x+1)-f(x)=2x-1$.

(1) Find the analytical expression of the function $f(x)$;

(2) The function $g(x)=2^{f(x)+\lambda x}$ is monotonic in the interval $[-1, 2]$, find the range of $\lambda$;

(3) Find the range of the function $y=f(\sin x)$.

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