
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

An arithmetic progression, commonly referred to as an A.P., is a sequence in which each term, starting from the second term, is equal to the sum of the previous term and a fixed value $r$ called the common difference. For instance, the sequence below is an arithmetic progression with the initial term 3 and common difference 4:

$$
a_{1}=3, a_{2}=7, a_{3}=11, a_{4}=15, a_{5}=19, a_{6}=23, a_{7}=27, a_{8}=31, a_{9}=35, \ldots
$$

We denote the position number $i$ with the symbol $a_{i}$.

a) If the first term of an arithmetic progression is 2 and its common difference is 3, what is the value of the fourth term?

b) João's teacher asked him to calculate the eleventh term of an arithmetic progression. Unfortunately, he forgot the initial term and the common difference. The only information he remembered was:

$$
\begin{aligned}
a_{4}+a_{7}+a_{10} & =207 \\
a_{5}+a_{6}+a_{7}+a_{8}+a_{9}+a_{10}+a_{11} & =553
\end{aligned}
$$

What is the value of the eleventh term?

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