
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

In the cells of a $2 \times 35$ table (2 rows, 35 columns), there are non-zero real numbers placed such that all numbers in the top row are distinct. For any two numbers in the same column, the following condition is satisfied: one number is the square of the other.

(a) (1 point) What is the maximum number of negative numbers that can be in this table?

(b) (3 points) What is the minimum number of distinct numbers that can be in the bottom row?

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