
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 equation about $x$: $$\log_{2}(x^{2}-2x+5)-|2a-1|=0$$ has solutions when $x \in [0, 3]$.
(Ⅰ) Find the set $A$ of values taken by the positive real number $a$;
(Ⅱ) If $t^2-at-3 \geq 0$ holds for any $a \in A$, find the range of values for the real number $t$.

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