
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
For every integer  $ n \geq 2$  determine the minimum value that the sum  $ \sum^n_{i\equal{}0} a_i$  can take for nonnegative numbers  $ a_0, a_1, \ldots, a_n$  satisfying the condition  $ a_0 \equal{} 1,$   $ a_i \leq a_{i\plus{}1} \plus{} a_{i\plus{}2}$  for  $ i \equal{} 0, \ldots, n \minus{} 2.$ 

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