
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 \equal{} 11^{11}, \, a_2 \equal{} 12^{12}, \, a_3 \equal{} 13^{13}$ , and  $ a_n \equal{} |a_{n \minus{} 1} \minus{} a_{n \minus{} 2}| \plus{} |a_{n \minus{} 2} \minus{} a_{n \minus{} 3}|, n \geq 4.$  Determine  $ a_{14^{14}}$ .

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