
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 line \( x = \sqrt{3} / 2 \), find the point \( M \) through which two tangents to the graph of the function \( y = x^2 / 2 \) pass, with the angle between them equal to \( 60^\circ \) (without using the derivative).

Given:
\[ y = \frac{x^2}{2} \]
\[ M\left(\frac{\sqrt{3}}{2}, y_0\right) \]

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