
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 $f(x)=|2x+1|+|2x-3|$.

1. Find the range of values for the real number $a$ such that the solution set of the inequality $f(x) < |1-2a|$ with respect to $x$ is not empty.
2. Find the range of values for the real number $m$ such that the quadratic equation $t^{2}+2 \sqrt {6}t+f(m)=0$ with respect to $t$ has real roots.

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