
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
An ant walks inside a \(18 \mathrm{~cm}\) by \(150 \mathrm{~cm}\) rectangle. The ant's path follows straight lines which always make angles of \(45^{\circ}\) to the sides of the rectangle. The ant starts from a point \(X\) on one of the shorter sides. The first time the ant reaches the opposite side, it arrives at the midpoint. Find the distance, in centimetres, from \(X\) to the nearest corner of the rectangle.

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