
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
Write down the general formula of a sequence $\{a_{n}\}$ that satisfies the following properties: $a_{n}=$____.<br/>$(1)$ The sequence $\{a_{n}\}$ is an infinite geometric sequence;<br/>$(2)$ The sequence $\{a_{n}\}$ is not monotonic;<br/>$(3)$ The sequence $\{|a_{n}|\}$ is monotonically decreasing.

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