
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 \( y = -\frac{5}{3} \), find the point \( M \) through which two tangent lines to the graph of the function \( y = \frac{x^{2}}{2} \) pass, and the angle between these tangents is \( 60^\circ \).

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