
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
In a right triangle \(ABC\) with \(\angle ABC = 90^\circ\), three pairs of parallel lines \(AB \parallel A'B'\), \(BC \parallel B'C'\), and \(AC \parallel A'C'\) are drawn such that the distance between each pair of parallel lines is 1 unit. Given that \(AC = 10\), \(AB = 8\), and \(BC = 6\), find the maximum distance from a point on triangle \(A'B'C'\) to the sides of triangle \(ABC\).

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