
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 $f(x) = 2^x + 3x - 7$, $g(x) = \ln x + 2x - 6$. If the real numbers $a$, $b$ satisfy $f(a) = 0$, $g(b) = 0$, arrange the following expressions in ascending order: $f(b)$, $g(a)$, $0$.

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