
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 vertices of a square are located on the base of an isosceles triangle, and the other two vertices are on its lateral sides. Find the side length of the square if the base of the triangle is $a$ and the angle at the base is $30^{\circ}$.

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