
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 an arithmetic sequence $\{a_{n}\}$ with the sum of the first $n$ terms as $S_{n}$ and a common difference of $d=2$.<br/>$(1)$ If $S_{10}=100$, find the general formula for $\{a_{n}\}$;<br/>$(2)$ From the set $\{a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$, $a_{5}$, $a_{6}\}$, choose any $3$ elements. Let event $A$ be the occurrence of these $3$ elements forming an arithmetic sequence. Find the probability $P\left(A\right)$ of event $A$ occurring.

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