
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
On a rectangular plot, a house is being built. In a right-angled coordinate system defined by two adjacent sides of the plot, the coordinates of two adjacent corners of the house are: $(1 ; 14),(17 ; 2)$. Where should the other two corners of the house be staked out if they want the shorter walls of the house to be half as long as the staked-out wall?

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