
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 $m\in\mathbb{R}$, let the proposition $P$ be: for any $x\in[-1,1]$, the inequality $-x^2+3m-1 \leq 0$ always holds; let the proposition $Q$ be: there exists $x\in[-1,1]$ such that $m-ax\leq 0$ holds.
(i) When $a=1$, both $P$ and $Q$ are false, and at least one of $P$ or $Q$ is true, find the range of $m$.
(ii) If $P$ is a sufficient but not necessary condition for $Q$, find the range of the real number $a$.

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