
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
In the arithmetic sequence $\left\{a_n\right\}$, if $a_2=4$ and $1+a_3$, $a_6$, $4+a_{10}$ form a geometric sequence, then the common difference $d=$_______

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