
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
The function $f(x)$ is defined as follows:
$$f(x)= \begin{cases} (x-a)^{2},x\leqslant 0 \\ x+ \frac {1}{x}+a,x > 0. \end{cases}$$
Determine the range of values for $a$ if $f(0)$ is the minimum value of $f(x)$.

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