
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 $a>0$, $b>0$, $c>0$, and the function $f(x) = |x+a| + |x-b| + c$ has a minimum value of 4.  
(1) Find the value of $a+b+c$;  
(2) Find the minimum value of $\frac{1}{4}a^2 + \frac{1}{9}b^2 + c^2$.

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