
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 function f(x) is an even function defined on R, and when x≤0, f(x)=x^2+2x.
(1) Find the analytic expression of function f(x) (x∈R);
(2) If function g(x)=f(x)-2ax+1 (x∈[1,2]), find the expression of the minimum value h(a) of function g(x).

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