
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
Given three real numbers \( x, y, \) and \( z \), which satisfy the equations \( (x+y)^{2}+(y+z)^{2}+(x+z)^{2}=94 \) and \( (x-y)^{2}+(y-z)^{2}+(x-z)^{2}=26 \), find:
1. The value of \( x y + y z + x z \);
2. The value of \( (x + 2y + 3z)^{2} + (y + 2z + 3x)^{2} + (z + 2x + 3y)^{2} \).

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