
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: $a + b = 1$; $a^2 + b^2 = 3$; $a^3 + b^3 = 4$; $a^4 + b^4 = 7$; $a^5 + b^5 = 11$; ...; then $a^{10} + b^{10} = \boxed{\text{?}}$.

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