
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 the following equations: observe each equation: $a+b=1$, $a^{2}+b^{2}=3$, $a^{3}+b^{3}=4$, $a^{4}+b^{4}=7$, $a^{5}+b^{5}=11$, $...$, then according to this pattern, we can get $a^{6}+b^{6}=$ $\_\_\_\_\_\_$.

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