
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 \(ABCD\), \(AB = 10\) cm and \(BC = 20\) cm. Point \(M\) moves from point \(B\) towards point \(A\) along edge \(AB\) at a speed of 1 cm per second, and point \(N\) moves from point \(C\) towards point \(B\) along edge \(BC\) at a speed of 1 cm per second. At the 10th second, the distance traveled by the midpoint \(P\) of the line segment \(MN\) is ______.

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