
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
Define a sequence of positive integers  $\{a_n\}$  through the recursive formula: $a_{n+1}=a_n+b_n(n\ge 1)$ ,where  $b_n$  is obtained by rearranging the digits of  $a_n$  (in decimal representation) in reverse order (for example,if  $a_1=250$ ,then  $b_1=52,a_2=302$ ,and so on). Can  $a_7$  be a prime?

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