
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
Two points \( A \) and \( B \), initially separated by a distance \( a \), simultaneously started moving along different sides of a right angle towards its vertex, each with the same constant speed \( v \). Point \( B \) reaches the vertex \( t \) units of time before point \( A \) (all measurements are in the same unit system). Determine how long point \( A \) was in motion. What value should be assigned to \( a \) for the sought time to be the least possible?

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