
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 number 10.105 is written with 1991 digits of 9 between two 1s. That is:
\[ 
1 \underbrace{99 \cdots 991}_{1991 \text{ digits of } 9}
\]

Questions:
(1) Where should "+" symbols be placed to obtain the minimum possible sum?
(2) Where should "×" symbols be placed to obtain the maximum possible product?
(The 54th Moscow Mathematical Olympiad, 1991)

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