
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 square is inscribed in an isosceles right triangle such that one vertex of the square is located on the hypotenuse, the opposite vertex coincides with the right angle vertex of the triangle, and the other vertices lie on the legs. Find the side of the square if the leg of the triangle is $a$.

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