
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 that $a>0$, $b>0$, $c>0$, the minimum value of the function $f(x)=|x+a|+|x-b|+c$ is 4.
(I) Find the value of $a+b+c$;
(II) 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