
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  $N$  be the number of functions  $f$  from  $\{1, 2, \dots, 101 \} \rightarrow \{1, 2, \dots, 101 \}$  such that  $f^{101}(1) = 2.$  Find the remainder when  $N$  is divided by  $103.$ 

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