
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
Let $A=\{x \mid 2 \leq x \leq 6\}$ and $B=\{x \mid 2a \leq x \leq a+3\}$. If $A \cup B = A$, find the range of the real number $a$.

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