
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
Read the following solution process: Given $x+x^{-1}=3$, find the value of $x^{3}+x^{-3}$. Solution: Since $(x+x^{-1})^{2}=x^{2}+x^{-2}+2=9$, therefore $x^{2}+x^{-2}=7$, hence $x^{3}+x^{-3}=(x^{2}+x^{-2})(x+x^{-1})-(x+x^{-1})=7\times 3-3=18$. Based on the above solution process, answer the following question: Given $x+x^{-1}=3$, find the value of $x^{5}+x^{-5}$.

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