
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 the function \( f(x) = \left| \log_{2} x \right| \). Real numbers \( a \) and \( b \) (where \( a < b \)) satisfy the following conditions:
\[
\begin{array}{l}
f(a+1) = f(b+2), \\
f(10a + 6b + 22) = 4
\end{array}
\]

Find \( ab \).

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