
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
Initially five variables are defined:  $a_1=1, a_2=0, a_3=0, a_4=0, a_5=0.$  On a turn, Evan can choose an integer  $2 \le i \le 5.$  Then, the integer  $a_{i-1}$  will be added to  $a_i$ . For example, if Evan initially chooses  $i = 2,$  then now  $a_1=1, a_2=0+1=1, a_3=0, a_4=0, a_5=0.$  Find the minimum number of turns Evan needs to make  $a_5$  exceed  $1,000,000.$ 

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