
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
Call a positive integer  $N$  a  $\textit{7-10 double}$  if the digits of the base-7 representation of  $N$  form a base-10 number that is twice  $N.$   For example, 51 is a 7-10 double because its base-7 representation is 102.  What is the largest 7-10 double?

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