
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
Determine how many measurements of tree cross-sections need to be taken in a large area so that the average diameter of the trees differs from the true value $a$ by no more than 2 cm with a probability of at least 0.95. The standard deviation of the tree cross-sections does not exceed $10 \mathrm{~cm}$ and the measurements are taken without error.

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