
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 thin lens with a focal length of $F=150$ cm is illuminated by a parallel beam of light perpendicular to the lens. A screen is placed behind the lens, on which a circular spot of a certain diameter is visible. If the screen is moved 40 cm, the same diameter spot is visible on the screen again. Determine the initial distance from the lens to the screen. (15 points)

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