
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 $$\frac {1}{3}$$≤a≤1, if the function f(x)=ax<sup>2</sup>-2x+1 has its maximum value M(a) and minimum value N(a) in the interval [1,3], let g(a)=M(a)-N(a).
(1) Find the expression for g(a);
(2) Describe the intervals where g(a) is increasing and decreasing (no proof required), and find the minimum value of g(a).

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