
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 old woman Shapoklyak concluded a futures contract, according to which Gena agreed to invest in the 1st project an amount equal to \(p_{1}>0\) thousand rubles, and after a year to receive \(x_{1}\) thousand rubles, such that

\[ 
4 x_{1} - 3 p_{1} - 44 = 0 
\]

At the same time, Gena agreed to invest in the 2nd project an amount equal to \(p_{2}>0\) thousand rubles, and after a year to receive \(x_{2}\) thousand rubles, such that

\[ 
p_{2}^{2} - 12 p_{2} + x_{2}^{2} - 8 x_{2} + 43 = 0 
\]

According to the terms of the contract, the parameters \(p_{1}, x_{1}, p_{2}, x_{2}\) were chosen so that the quantity

\[ 
d = \sqrt{(x_{1} - x_{2})^{2} + (p_{1} - p_{2})^{2}} 
\]

was minimized. Determine:

1. The minimum value of \(d\);
2. Whether the deal is profitable for Gena, and find the amount of profit or loss for Gena based on this deal.

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