
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 \( f(x) = \frac{a x^2}{e^x} \), the line \( y = \frac{1}{e} x \) is a tangent to the curve \( y = f(x) \).

(1) Find the value of the real number \( a \).

(II) Using \( \min \{m, n\} \) to indicate the minimum of \( m \) and \( n \), let \( g(x) = \min \left\{ f(x), x - \frac{1}{x} \right\} (x > 0) \). If the function \( h(x) = g(x) - c x^2 \) is an increasing function, find the range of values for the real number \( c \).

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