
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  $a$ ,  $b$ ,  $c$ , and  $d$  be positive real numbers such that
\[a^2 + b^2 - c^2 - d^2 = 0 \quad \text{and} \quad a^2 - b^2 - c^2 + d^2 = \frac{56}{53}(bc + ad).\]
Let  $M$  be the maximum possible value of  $\tfrac{ab+cd}{bc+ad}$ . If  $M$  can be expressed as  $\tfrac{m}{n}$ , where  $m$  and  $n$  are relatively prime positive integers, find  $100m + n$ .

*Proposed by Robin Park*

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