
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

Find the minimum value of the expression 

$$
\frac{|a-3b-2| + |3a-b|}{\sqrt{a^2 + (b+1)^2}}
$$

for \(a, b \geq 0\).

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