
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 $\overset{→}{e}_1$ and $\overset{→}{e}_2$ are two non-collinear vectors, $\overset{→}{AB}=2\overset{→}{e}_1+k\overset{→}{e}_2$, $\overset{→}{CB}=\overset{→}{e}_1+3\overset{→}{e}_2$, and $\overset{→}{CD}=2\overset{→}{e}_1-\overset{→}{e}_2$,

(1) Find the value of $k$ if points $A$, $B$, and $D$ are collinear.

(2) If $\overset{→}{MN}=2\overset{→}{e}_1+13\overset{→}{e}_2$, find the decomposition of $\overset{→}{MN}$ using $\overset{→}{CB}$ and $\overset{→}{CD}$ as the basis.

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