
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]


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Given a sequence ${{a_n}}$, if $\forall m,n \in \mathbb{N^*}(m \neq n)$, it always satisfies $\frac{{{a_m} - {a_n}}}{{m - n}} \geqslant t(t$ is a constant), then the sequence ${{a_n}}$ is said to have property $P(t)$.

(i) If the general term of the sequence ${{a_n}}$ is ${{a_n} = {n^2}}$, and it has property $P(t)$, then the maximum value of $t$ is ___;

(ii) If the general term of the sequence ${{a_n}}$ is ${{a_n} = {n^2} - \frac{a}{n}}$, and it has property $P(7)$, then the range of the real number $a$ is ___.

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