
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
The products of certain pairs of numbers can be expressed in a unique pattern:
- $13 \times 17 = 221$ can be expressed as $100 \times 1 \times (1 + 1) + 21$;
- $23 \times 27 = 621$ can be expressed as $100 \times 2 \times (2 + 1) + 21$;
- In the 21st century, $33 \times 37 = 1221$ can be expressed as $100 \times 3 \times (3 + 1) + 21$;
- $43 \times 47 = 2021$ can be expressed as $100 \times 4 \times (4 + 1) + 21$; …

Based on the pattern above, fill in the blanks:
1. $83 \times 87$ can be expressed as _______;
2. $(10n+3)(10n+7)$ can be expressed as _______.

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