
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
The function $f(x) = ax^n(1-x)$ $(x > 0, n \in \mathbb{N}^*)$, when $n = -2$, the maximum value of $f(x)$ is $\frac{4}{27}$.  
(1) Find the value of $a$;  
(2) If the equation $f(x) - m = 0$ has two positive real roots, find the range of values for $m$.

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