
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
Let the integer sequence $a_{1}, a_{2}, \cdots, a_{k}$ have a length of $k$, where $1 \leqslant a_{i} \leqslant 4$ for $i=1,2, \cdots, k$. If the sequence satisfies the condition: "if $a_{i}=a_{j}$ and $a_{i+1}=a_{j+1}$, then $i=j$," then what is the maximum value of $k$?

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