
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: $8x^2y^{1+a}$ is a monomial of degree 5 in terms of $x$ and $y$. Find the value of the following algebraic expressions:  
(1) $a^3+1$; (2) $(a+1)(a^2-a+1)$; (3) Based on (1) and (2), what discoveries or thoughts do you have?

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