
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
The diagonals of an inscribed quadrilateral $\mathrm{ABCD}$ are perpendicular. Perpendiculars dropped from vertices $\mathrm{B}$ and $\mathrm{C}$ to side $\mathrm{AD}$ intersect diagonals $\mathrm{AC}$ and $\mathrm{BD}$ at points $\mathrm{M}$ and $\mathrm{N}$, respectively. Find the length of $\mathrm{MN}$ if $\mathrm{BC}=2$.

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