
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
Find all finite sequences  $(x_0, x_1, \ldots,x_n)$  such that for every  $j$ ,  $0 \leq j \leq n$ ,  $x_j$  equals the number of times  $j$  appears in the sequence.

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