
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 a regular tetrahedron  $OABC$  with side length 1. Let  $D,\ E$  be the midpoints of the sides  $AB,\ OC$  respectively.
Find the scalar product of two vectors  $\overrightarrow{DE}$  and  $\overrightarrow{AC}$ .

2012 Tokyo Institute of Technology entrance exam, problem 1-A

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