
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]


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As shown, \(U\) and \(C\) are points on the sides of triangle \(MN H\) such that \(MU = s\), \(UN = 6\), \(NC = 20\), \(CH = s\), and \(HM = 25\). If triangle \(UNC\) and quadrilateral \(MUCH\) have equal areas, what is \(s\)?

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