
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
It is known that the graphs of the functions $f(x)$ and $g(x)$ are symmetric with respect to the origin, and $f(x) = x^2 + x$.
(Ⅰ) Find the analytic expression for the function $g(x)$;
(Ⅱ) If $h(x) = g(x) - \lambda f(x) + 1$ is an increasing function on the interval $[-1, 1]$, determine the range of values for the real number $\lambda$.

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