
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 functions f(x) and g(x) are an even function and an odd function defined on R, respectively, and f(x) + g(x) = x^2 - x + 1.
(1) Find the analytical expressions for functions f(x) and g(x).
(2) Let G(x) = f(x) + a|g(x) + 1|, if G(x) ≥ 3/2 holds for any real number x, find the range of real number a.

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