
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
Let  $\lambda$  be a real number. Suppose that if \(ABCD\) is any convex cyclic quadrilateral such that \(AC=4\), \(BD=5\), and \(\overline{AB}\perp\overline{CD}\), then the area of  $ABCD$  is at least  $\lambda$ . Then the greatest possible value of  $\lambda$  is  $\frac{m}{n}$ , where  $m$  and  $n$  are positive integers with  $\gcd(m,n)=1$ . Compute  $100m+n$ .

*Proposed by Eric Shen*

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