
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 the functions f(x) = 2cos2x, g(x) = a - 4$\sqrt {3}$sinx.
(1) When a=0, let h(x) = f(x) + g(x), find the maximum and minimum values of h(x).
(2) When f(x) ≥ g(x) is always true for x ∈ [n, m], the maximum value of m - n is $\frac {5π}{3}$, find the value of a.

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