
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 camera lens has a focal length of $50 \mathrm{~mm}$ and a diameter of $20 \mathrm{~mm}$. The lens is set to focus on an object $5 \mathrm{~m}$ away. What is the maximum and minimum distance within which the image of a point is smaller than a $0,05 \mathrm{~mm}$ diameter spot on the film? How does this range change if the lens diameter is reduced to $10 \mathrm{~mm}$?

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