
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
The "2023 MSI" Mid-Season Invitational of "League of Legends" is held in London, England. The Chinese teams "$JDG$" and "$BLG$" have entered the finals. The finals are played in a best-of-five format, where the first team to win three games wins the championship. Each game must have a winner, and the outcome of each game is not affected by the results of previous games. Assuming that the probability of team "$JDG$" winning a game is $p (0 \leq p \leq 1)$, let the expected number of games be denoted as $f(p)$. Find the maximum value of $f(p)$.

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