
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) If the inequality $f(x) > |1-3a|$ always holds for $x$, find the range of the real number $a$;  
(2) If the quadratic equation in $t$, $t^{2}-4 \sqrt {2}t+f(m)=0$, has real roots, find the range of the real number $m$.

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