
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
In rectangle  $ABCD$ , point  $M$  is the midpoint of  $AB$  and  $P$  is a point on side  $BC$ . The perpendicular bisector of  $MP$  intersects side  $DA$  at point  $X$ . Given that  $AB = 33$  and  $BC = 56$ , find the least possible value of  $MX$ .

*Proposed by Michael Tang*

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