
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
In the sequence ${a_n}$, $a_1=1$, $a_n+a_{n+1}=pn+1$, where $p$ is a constant.
(1) If $a_1$, $a_2$, $a_4$ form a geometric sequence, find the value of $P$:
(2) Does there exist a $p$ such that the sequence ${a_n}$ is an arithmetic sequence? Explain your reasoning.

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