
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
Suppose  $a$  is a real number such that  $3a + 6$  is the greatest integer less than or equal to  $a$  and  $4a + 9$  is the least integer greater than or equal to  $a$ . Compute  $a$ .

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