
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  $a_1,a_2,\cdots,a_{100}\geq  0$  such that  $\max\{a_{i-1}+a_i,a_i+a_{i+1}\}\geq i $  for any  $2\leq i\leq 99.$  Find the minimum of  $a_1+a_2+\cdots+a_{100}.$ 

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