
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

Crocodile Gena and the old lady Shapoklyak entered into a futures contract, according to which Gena agreed to invest in the 1st project an amount equal to \( p_1 > 0 \) thousand rubles and receive \( x_1 \) thousand rubles after a year such that

\[ 4 x_1 - 3 p_1 - 44 = 0 \]

Gena also agreed to invest in the 2nd project an amount equal to \( p_2 > 0 \) thousand rubles and receive \( x_2 \) thousand rubles after a year such that

\[ p_2^2 - 12 p_2 + x_2^2 - 8 x_2 + 43 = 0 \]

According to the terms of the deal, the parameters \( p_1, x_1, p_2, x_2 \) were chosen to minimize the value of

\[ d = \sqrt{(x_1 - x_2)^2 + (p_1 - p_2)^2} \]

Determine:

1. The minimum value of \( d \).
2. Whether the deal is profitable for Gena. Find the amount of profit or loss for Gena if he agrees to this deal.

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