
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
There is an arrangement of three equilateral triangles, each side is 1 inch, placed with their bases on a line. The center triangle is lifted, rotated 60 degrees, and is then centered and lowered into its original position until it touches both of the adjoining triangles. Determine the distance from point $P$ (the highest vertex of the rotated triangle) from the line on which the bases of the original triangles were placed.
- **A)** $\frac{1}{2}$
- **B)** $\frac{\sqrt{3}}{2}$
- **C)** $\sqrt{3}$
- **D)** $1$

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