
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 100 numbers \(a_{1}, a_{2}, a_{3}, \ldots, a_{100}\) that satisfy the conditions:

\[
\begin{array}{r}
a_{1}-4 a_{2}+3 a_{3} \geqslant 0, \\
a_{2}-4 a_{3}+3 a_{4} \geqslant 0, \\
a_{3}-4 a_{4}+3 a_{5} \geqslant 0, \\
\ldots \\
\ldots \\
\ldots \\
a_{99}-4 a_{100}+3 a_{1} \geqslant 0, \\
a_{100}-4 a_{1}+3 a_{2} \geqslant 0
\end{array}
\]

It is known that \(a_{1}=1\). Determine \(a_{2}, a_{3}, \ldots, a_{100}\).

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