
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|x-a| + 2x - 3,
1. Find the maximum and minimum values of the function f(x) when a = 4 and 2 ≤ x ≤ 5.
2. Find the range of the real number a such that f(x) ≤ 2x - 2 always holds true when x ∈ [1, 2].

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