
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
Given a rectangle \(ABCD\). A line passing through vertex \(A\) and point \(K\) on side \(BC\) divides the entire rectangle into two parts, one of which has an area 5 times smaller than the other. Find the length of segment \(KC\) if \(AD = 60\).

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