
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 a function $f\left(x\right)$ with a domain of $R$ that satisfies the following three conditions:<br/>① The graph of the function does not pass through the origin;<br/>② For any $x\in R$, $f\left(x\right)=f\left(-x\right)$;<br/>③ For any $x\in R$, $f\left(x+\pi \right)=f\left(x\right)$.<br/>Please write an expression for the function $f\left(x\right)=$____$($the answer is not unique, provide one possible expression).

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