
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  $a_{1}={11}^{11}$ ,  $a_{2}={12}^{12}$ ,  $a_{3}={13}^{13}$ , and \[a_{n}= \vert a_{n-1}-a_{n-2}\vert+\vert a_{n-2}-a_{n-3}\vert, n \ge 4.\] Determine  $a_{{14}^{14}}$ .

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