
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 that $a$, $b$, $c$, $d$ form an arithmetic sequence, and the function $y=\ln(x+2)-x$ has a maximum value at $x=b$, where the maximum value is $c$, calculate the sum $b+d$.

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