
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's play a number game:  
Step 1: Take a natural number, $n_1 = 5$, calculate $n_1^2 + 1$ to get $a_1$;  
Step 2: Calculate the sum of the digits of $a_1$ to get $n_2$, then calculate $n_2^2 + 1$ to get $a_2$;  
Step 3: Calculate the sum of the digits of $a_2$ to get $n_3$, then calculate $n_3^2 + 1$ to get $a_3$;  
And so on, then $a_{2009} = \ $

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