
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
A sequence is called an *arithmetic progression of the first order* if the differences of the successive terms are constant. It is called an *arithmetic progression of the second order* if the differences of the successive terms form an arithmetic progression of the first order. In general, for  $k\geq 2$ , a sequence is called an *arithmetic progression of the  $k$ -th order* if the differences of the successive terms form an arithmetic progression of the  $(k-1)$ -th order.
The numbers
\[4,6,13,27,50,84\]
are the first six terms of an arithmetic progression of some order. What is its least possible order? Find a formula for the  $n$ -th term of this progression.

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