
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 function f(x) = -$\frac{1}{2}$x² + $\frac{1}{2}$a(5-a)x + c.
(1) If c=16, solve the inequality f(2) > 0 for a;
(2) If a=4, find the range of real number c such that f(x) < 0 holds true for any x ∈ (-∞, 1].

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