
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
In a regular quadrilateral pyramid $SABC D$, the length of each edge is $a$. Point $M$ lies on $SC$ such that $SM : MC = 2 : 1$. Find the angle between vectors $\overline{DC}$ and $\overline{AM}$.

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