
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 $f(x)$ defined on $\mathbb{R}$ that satisfies: $f\left( x+1 \right)=\frac{1}{f(x)}$, and $f(x)=2^{x}$ when $x\in \left( 0,1 \right]$, determine the value of $f\left( \log _{2}9 \right)$.

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