
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 $f(x)=x+1$, $g(x)=2^{|x+2|}+a$, if for any $x_{1}\in [3,4]$, there exists $x_{2}\in [-3,1]$, such that $f(x_{1})\geq g(x_{2})$, determine the possible values of real number $a$.

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