
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 $f(x)=|x-10|+|x-20|$, and it satisfies $f(x) < 10a+10 (a∈R)$ where the solution set is not empty.

1. Find the range of values for the real number $a$.
2. Find the minimum value of $a+ \frac {4}{a^{2}}$.

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