
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
The sequence \( a_n \) is defined by \( a_1 = 1111 \), \( a_2 = 1212 \), \( a_3 = 1313 \), and \( a_{n+3} = | a_{n+2} - a_{n+1} | + | a_{n+1} - a_n | \). Find \( a_{n} \), where \( n = 1414 \).

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