
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 parabola $E: y^2 = 2px$ ($p>0$) with focus $F$, and $OF$ (where $O$ is the origin) as one diagonal of the rhombus $OBFC$, the other diagonal $BC$ has a length of 2, and $B$, $C$ are on the parabola $E$, determine the value of $p$.

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