
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 $f(x)$ and $g(x)$ are odd functions, if $H(x) = af(x) + bg(x) + 1$ has a maximum value of 5 in the interval $(0, +\infty)$, then the minimum value of $H(x)$ in the interval $(-\infty, 0)$ is __.

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