
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 $f(x)=|x-a|+2|x+b| (a > 0, b > 0)$ with a minimum value of $1$.
1. Find the value of $a+b$.
2. If $m \leq \frac{1}{a} + \frac{2}{b}$ always holds, find the maximum value of the real number $m$.

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