
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  $f(x)$  be a function such that  $f(1) = 1234$ ,  $f(2)=1800$ , and  $f(x) = f(x-1) + 2f(x-2)-1$  for all integers  $x$ . Evaluate the number of divisors of
    \[\sum_{i=1}^{2022}f(i)\]

*2022 CCA Math Bonanza Tiebreaker Round #4*

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