
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 that $M$ is any point on the segment $AB$, $O$ is a point outside the line $AB$, $C$ is the symmetric point of $A$ with respect to point $O$, and $D$ is the symmetric point of $B$ with respect to point $C$. If $\overrightarrow{OM}=x\overrightarrow{OC}+y\overrightarrow{OD}$, then $x+3y=\_\_\_\_\_\_$.

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