
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 woman Shapoklyak made a futures deal 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

\[ 
3 x_{1} - 4 p_{1} - 30 = 0 
\]

Gena also 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

\[ 
p_{2}^{2} - 12 p_{2} + x_{2}^{2} - 14 x_{2} + 69 = 0 
\]

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

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

was as small as possible. 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 the deal.

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