
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
For a parabola with its vertex at the origin, given the following conditions:

① The focus is on the y-axis; ② The focus is on the x-axis; ③ The distance from the point on the parabola with an x-coordinate of 1 to the focus is 6; ④ The length of the latus rectum is 5; ⑤ A perpendicular line is drawn from the origin to a certain line passing through the focus, and the foot of the perpendicular is at the coordinate (2,1). The conditions that make the equation of the parabola $y^2=10x$ are __________. (Please fill in the appropriate condition numbers)

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