
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
The area of an isosceles triangle is $\frac{1}{3}$ of the area of a square constructed on the base of the given triangle. The lengths of the legs of the triangle are shorter than the length of its base by 1 cm. Find the lengths of the sides and the height of the triangle drawn to the base.

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