
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 parabolic arch has a height of $20$ inches and a span of $50$ inches. Calculate the height of the arch at the point $10$ inches from the center. Additionally, find where along the span from the center (to the left or right) the width equals the height of the arch at that point.

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