
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 that the quadratic function $f(x)$ has two zeros at $0$ and $-2$, and the minimum value of $f(x)$ is $-1$, the graph of function $g(x)$ is symmetric to the graph of $f(x)$ with respect to the origin.

(1) Find the expressions for $f(x)$ and $g(x)$;  
(2) If $h(x) = f(x) - \lambda g(x)$ is an increasing function on the interval $[-1,1]$, find the range of the real number $\lambda$.

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