
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| + 2|x-1|,

1. Find the minimum value of f(x);
2. If the solution set of the inequality f(x) + x - a < 0 is (m, n), and n - m = 6, find the value of a.

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