
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
A vertically positioned structure consists of two identical masses connected by a spring (see the drawing). An impact causes the upper mass to start moving with an initial velocity \( V_{1} \) at an angle \( \beta \) to the horizontal, and the lower mass to start moving with a velocity \( V_{2} \) at an angle \( \alpha \) to the horizontal. To what maximum height relative to its initial position will point \( A \), the center of the spring, rise?

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