
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 that the domain of the function $f(x)$ is $D$, the function satisfies the following conditions:
1. $f(x)$ is a monotonic function within $D$;
2. If there exists an interval $[a, b] \subseteq D$ such that the range of $f(x)$ on $[a, b]$ is $[2a, 2b]$, then the function $f(x)$ is called a "successful function".
Determine the range of values for $t$ if the function $f(x) = \log_{c}(c^{4x} + 3t)\,(c > 0, c \neq 1)$ is a "successful function".

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