
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
Suppose three non-zero and distinct real numbers $a$, $b$, $c$ satisfy $\frac{1}{a} + \frac{1}{b} = \frac{2}{c}$, then we say $a$, $b$, $c$ are harmonic; if they satisfy $a + c = 2b$, then we say $a$, $b$, $c$ are arithmetic. If the elements $a$, $b$, $c$ in set $P$ are both harmonic and arithmetic, then we call set $P$ a "good set". If set $M = \{x ||x| \leqslant 2014, x \in \mathbb{Z}\}$, set $P = \{a, b, c\} \subseteq M$, then:
(1) The maximum value of the elements in the "good set" $P$ is $\_\_\_\_\_\_$;
(2) The number of "good sets" $P$ is $\_\_\_\_\_\_$.

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