
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
The teacher needed to come up with equations for a test. She wrote down all equations of the form

$$
a \cdot x + b = 13
$$

where \(a\) and \(b\) are single-digit natural numbers. From these, she selected the equations whose root \(x\) was 3. She put one equation into each group. What is the maximum number of groups that could be formed?

(K. Pazourek)

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