
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 sequence $\left\{{\frac{1}{{4{n^2}+4n-3}}}\right\}$, let $T_{n}$ denote the sum of the first $n$ terms. If the inequality $12T_{n} \lt 3a^{2}-a$ holds for all positive integers $n$, determine the range of the real number $a$.

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