
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 the functions $f(x)=λx^{2}+λx$, $g(x)=λx+ \ln x$, and $h(x)=f(x)+g(x)$, where $λ∈R$ and $λ≠ 0$.
(1) When $λ=-1$, find the maximum value of the function $g(x)$;
(2) Find the monotonic intervals of the function $h(x)$;
(3) Define the function $φ(x)= \begin{cases} f(x),x\leqslant 0 \\ g(x),x > 0.\end{cases}$. If for any given non-zero real number $x$, there exists a non-zero real number $t(t≠x)$ such that $φ′(x)=φ′(t)$ holds, find the range of values for the real number $λ$.

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