
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
For a sequence $A$ consisting of positive integers: $a_1, a_2, \ldots, a_n$, define the transformation $T_1$, which transforms sequence $A$ into sequence $T_1(A)$: $n, a_1-1, a_2-1, \ldots, a_n-1$; for a sequence $B$ consisting of non-negative integers: $b_1, b_2, \ldots, b_m$, define the transformation $T_2$, which sorts the elements of sequence $B$ in descending order and then removes all zero elements, resulting in sequence $T_2(B)$. Let $A$ be a finite sequence of positive integers, and let $A_{k+1} = T_2(T_1(A_k))$ ($k=0, 1, 2, \ldots$). If the sequence $A$ is $4, 2, 1$, then the sequence $A_1$ is.

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