
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 set $A = \{2, \log_{2}{t}\}$ and the set $B = \{x \mid y = \sqrt{(x-2)(5-x)}\}$,
(1) For an interval $[a, b]$, define the "length" of the interval as $b-a$. If the "length" of the interval $A$ is 3, find the value of the real number $t$.
(2) If $A \subsetneq B$, find the range of values for the real number $t$.

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