
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
Let $A = \{x \mid (8x-1)(x-1) \leq 0\}$ and $C = \{x \mid a < x < 2a+5\}$.

(1) If $\left(\frac{1}{4}\right)^t \in A$, determine the set $B$ of possible values for the real number $t$.

(2) Under the condition of (1), if $(A \cup B) \subseteq C$, find the range of values for the real number $a$.

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