
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
Rectangle $ABCD$ has dimensions $2$ units by $1$ unit. Points $E$ and $F$ are on sides $AB$ and $CB$, respectively, with $AE = 1/2$ unit and $CF = 1/2$ unit. When the rectangle is folded along lines $DE$ and $DF$, sides $AD$ and $CD$ coincide along the diagonal $BD$. Find the length of $BE$.

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