
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 an $18 \mathrm{~cm}$ 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. If the ant starts from a point $X$ on one of the shorter sides and reaches the opposite side at its midpoint for the first time, calculate 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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