
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 $\{a_{n}\}$, if $\{a_{n+1}-a_{n}\}$ forms an arithmetic sequence, then the original sequence $\{a_{n}\}$ is called a second-order arithmetic sequence. Generally, if $\{a_{n+1}-a_{n}\}$ forms a $K$-order arithmetic sequence, then the original sequence $\{a_{n}\}$ is called a $(K+1)$-order arithmetic sequence. Given a three-order arithmetic sequence with its first $7$ terms being $1$, $4$, $10$, $20$, $35$, $56$, $84$, the $8$th term of this sequence is ____.

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