
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
A polynomial  $p(x)$  with real coefficients is said to be *almeriense* if it is of the form:  $$  
p(x) = x^3+ax^2+bx+a $$  And its three roots are positive real numbers in arithmetic progression. Find all *almeriense* polynomials such that  $p\left(\frac{7}{4}\right) = 0$ 

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