
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 a sequence $\{a_n\}$, if for all $m, n \in \mathbb{N}^* (m \neq n)$, the inequality $\frac{a_m - a_n}{m - n} \geq t (t$ is a constant$)$ holds, then the sequence $\{a_n\}$ is said to have property $P(t)$.

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

(ii) If the general term of the sequence $\{a_n\}$ is $a_n = n^2 - \frac{a}{n}$ and it has property $P(10)$, find the range of values of the real number $a$.

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