
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
The famous mathematician Yang Hui of the Southern Song Dynasty in China delved into mathematics and wrote "Detailed Explanation of the Nine Chapters Algorithm," conducting in-depth research and summarization on mathematical operations. By analogy with the ideological methods in it, many calculation problems involving numbers and expressions can be solved. Now it is known that $a$ and $b$ are real numbers, and $a+b=3$, $ab=1$. Given that $a^{2}+b^{2}=7$, $a^{3}+b^{3}=18$, $a^{4}+b^{4}=47$, $\ldots$, find $a^{5}+b^{5}=$____.

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