
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
What are the last digits of the decimal representations of the following numbers:
1. \( 135^x + 31^y + 56^{x+y} \), where \( x \in \mathbb{N}, y \in \mathbb{N} \)?
2. \( 142 + 142^2 + 142^3 + \ldots + 142^{20} \)?
3. \( 34^x + 34^{x+1} + 34^{2x} \), where \( x \in \mathbb{N} \)?

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