
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 \(a_1, a_2, a_3, \ldots, a_{100}\) satisfying the conditions:
\[ 
a_1 - 4a_2 + 3a_3 \geq 0 
\]
\[ 
a_2 - 4a_3 + 3a_4 \geq 0 
\]
\[ 
a_3 - 4a_4 + 3a_5 \geq 0 
\]
\[ 
\vdots 
\]
\[ 
a_{99} - 4a_{100} + 3a_1 \geq 0 
\]
and 
\[ 
a_{100} - 4a_1 + 3a_2 \geq 0 
\]
It is known that \(a_1 = 1\). Determine \(a_2, a_3, \ldots, a_{100}\).

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