
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 $a > 0$, let proposition $p$: the function $f(x) = x^2 - 2ax + 1 - 2a$ has two distinct intersections with the x-axis in the interval $[0, 1]$; proposition $q$: $g(x) = |x - a| - ax$ has a minimum value. If the proposition $(\neg p) \land q$ is true, find the range of the real number $a$.

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