
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 $f\left( \frac{x}{2} \right) = -\frac{1}{8}x^3 + \frac{m}{4}x^2 - m$ ($0 < m < 20$).  
(1) Discuss the monotonicity of the function $f(x)$ in the interval $[2, 6]$.  
(2) If the curve $y = f(x)$ has tangents at two different points $A(x_1, f(x_1))$ and $B(x_2, f(x_2))$ that both pass through the point $(2, \lg \frac{1}{a})$, where $a \geq 1$, find the range of values for $m$.

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