
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 $f(x) = |x^2 - x| - ax$, 
(1) find the roots of the equation $f(x) = 0$ when $a = \frac{1}{3}$; 
(2) find the minimum value of the function $f(x)$ on the interval $[-2, 3]$ when $a \leq -1$.

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