
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 sequence $\left\{a_{n}\right\}$ with $k$ terms $(k\in N^{*})$, where $a_{1}=2$, define vectors $\overrightarrow {c_{n}}=(a_{n}, a_{n+1})$ and $\overrightarrow {d_{n}}=(n, n+1)$ for $n=1,2,3,\ldots, k-1$. If $|\overrightarrow {c_{n}}|=|\overrightarrow {d_{n}}|$, determine the number of sequences $\left\{a_{n}\right\}$ that satisfy this condition.

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