
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 the coordinate plane, a parabola \( y = x^2 \) is drawn. A point \( A \) is taken on the positive half of the \( y \)-axis, and two lines with positive slopes are drawn through it. Let \( M_1, N_1 \) and \( M_2, N_2 \) be the points of intersection with the parabola of the first and second lines, respectively. Find the ordinate of point \( A \), given that \( \angle M_1 O N_1 = \angle M_2 O N_2 \), where \( O \) is the origin.

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