
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
Given $A = "B" = \mathbb{R}$, $x \in A$, $y \in B$, for any $x \in A$, the function $x \rightarrow ax + b$ maps from $A$ to $B$. If the input values $1$ and $8$ correspond to the output values $3$ and $10$ respectively, then the output value corresponding to the input value $5$ is $\boxed{6}$.

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