
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
On a $100 \times 70$ meter football field, players have hidden the referee's whistle in the grass. The referee starts from one corner of the field and can step 1 meter in any direction. After each step, it is indicated to the referee whether he has gotten closer to the whistle or not. If the referee gets within 1 meter of the whistle, he will see it.

What should the referee do? Estimate the number of steps it will take for the referee to find the whistle if he was initially $d$ meters away from it.

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