
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 first term of the sequence $\{a_{n}\}$ is $a_{1}$, and it satisfies $12S_{n}=4a_{n+1}+5^{n}-13$, where $S_{n}$ is the sum of its first $n$ terms. If it always holds that $S_{n} \leq S_{4}$ for all $n \in \mathbb{N}^{*}$, then the range of values for $a_{1}$ is ______.

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