
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
In a right-angled coordinate system, the line \( x - d = 0 \) is given. Consider all conic sections whose focus is the origin and the corresponding directrix is the line \( x - d = 0 \). Draw tangents to these conic sections that are parallel to the line \( y = x \). What is the locus of the points of tangency?

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