
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
Given the pyramid $P-ABCD$, where the base $ABCD$ is a square and $E$ is the midpoint of $PD$, if $\overrightarrow{PA}=\overrightarrow{a}$, $\overrightarrow{PB}=\overrightarrow{b}$, $\overrightarrow{PC}=\overrightarrow{c}$, find the expression for $\overrightarrow{BE}$.

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