
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 the operation between two numbers $a$ and $b$, denoted as "$*$", to yield $4ab$, i.e., $a*b=4ab$. For example, $2*6=4\times2\times6=48$. If for any number $x$, it always holds that $a*x=x$, then $a=$    .

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