
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
Observe the following equations: $(a+b=1)$, $(a^{2}+b^{2}=3)$, $(a^{3}+b^{3}=4)$, $(a^{4}+b^{4}=7)$, $(a^{5}+b^{5}=11)$, $(...)$, find the value of $(a^{10}+b^{10})$ \_\_\_\_\_\_.

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