
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 $f(x)=| \frac {1}{2}x+1|+|x-1|$ where $x \in \mathbb{R}$, let its minimum value be $a$.
(1) Find $a$;
(2) If two positive numbers $m$ and $n$ satisfy $m^{2}+n^{2}=a$, find the minimum value of $\frac{1}{m} + \frac{1}{n}$.

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